Merge pull request keon#111 from yumyum414/master

added find all cliques alg

graph/find_all_cliques.py

@@ -0,0 +1,35 @@
+# takes dict of sets
+# each key is a vertex
+# value is set of all edges connected to vertex
+# returns list of lists (each sub list is a maximal clique)
+# implementation of the basic algorithm described in:
+# Bron, Coen; Kerbosch, Joep (1973), "Algorithm 457: finding all cliques of an undirected graph",
+
+
+def find_all_cliques(edges):
+    def expand_clique(candidates, nays):
+        nonlocal compsub
+        if not candidates and not nays:
+            nonlocal solutions
+            solutions.append(compsub.copy())
+        else:
+            for selected in candidates.copy():
+                candidates.remove(selected)
+                candidates_temp = get_connected(selected, candidates)
+                nays_temp = get_connected(selected, nays)
+                compsub.append(selected)
+                expand_clique(candidates_temp, nays_temp)
+                nays.add(compsub.pop())
+
+    def get_connected(vertex, old_set):
+        new_set = set()
+        for neighbor in edges[str(vertex)]:
+            if neighbor in old_set:
+                new_set.add(neighbor)
+        return new_set
+
+    compsub = []
+    solutions = []
+    possibles = set(edges.keys())
+    expand_clique(possibles, set())
+    return solutions